Chimera states in a chain of superdiffusively coupled neurons

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Abstract
Two- and three-component systems of superdiffusion equations describing the dynamics of action potential propagation in a chain of non-locally interacting neurons with Hindmarsh–Rose nonlinear functions have been considered. Non-local couplings based on the fractional Laplace operator describing superdiffusion kinetics are found to support chimeras. In turn, the system with local couplings, based on the classical Laplace operator, shows synchronous behavior. For several parameters responsible for the activation properties of neurons, it is shown that the structure and evolution of chimera states depend significantly on the fractional Laplacian exponent, reflecting non-local properties of the couplings. For two-component systems, an anisotropic transition to full incoherence in the parameter space responsible for non-locality of the first and second variables is established. Introducing a third slow variable induces a gradual transition to incoherence via additional chimera states formation. We also discuss the possible causes of chimera states formation in such a system of non-locally interacting neurons and relate them with the properties of the fractional Laplace operator in a system with global coupling.

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